TY - JOUR
T1 - Frequency-domain correlation
T2 - An asymptotically optimum approximation of quadratic likelihood ratio detectors
AU - Zhang, Wenyi
AU - Poor, H. Vincent
AU - Quan, Zhi
N1 - Funding Information:
Manuscript received April 30, 2009; accepted September 30, 2009. First published November 06, 2009; current version published February 10, 2010. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Jean-Yves Tourneret. The work of H. V. Poor was supported in part by the National Science Foundation by Grant CNS-06-25367.
PY - 2010/3
Y1 - 2010/3
N2 - An approximate implementation is formulated and analyzed for the detection of wide-sense stationary Gaussian stochastic signals in white Gaussian noise. For scalar processes, the approximate detector can be realized as the correlation between the periodogram of the observations and an appropriately selected spectral mask, and thus is termed the frequency-domain correlation detector. Through the asymptotic properties of Toeplitz matrices, it is shown that, as the length of the observation interval grows without bound, the frequency-domain correlation detector and the optimum quadratic detector achieve identical asymptotic performance, characterized by the decay rate of the miss probability under the Neyman-Pearson criterion. The frequency-domain correlation detector is further extended to the detection of vector-valued wide-sense stationary Gaussian stochastic signals, and the asymptotic optimality of its performance is established through the asymptotic properties of block Hermitian Toeplitz matrices.
AB - An approximate implementation is formulated and analyzed for the detection of wide-sense stationary Gaussian stochastic signals in white Gaussian noise. For scalar processes, the approximate detector can be realized as the correlation between the periodogram of the observations and an appropriately selected spectral mask, and thus is termed the frequency-domain correlation detector. Through the asymptotic properties of Toeplitz matrices, it is shown that, as the length of the observation interval grows without bound, the frequency-domain correlation detector and the optimum quadratic detector achieve identical asymptotic performance, characterized by the decay rate of the miss probability under the Neyman-Pearson criterion. The frequency-domain correlation detector is further extended to the detection of vector-valued wide-sense stationary Gaussian stochastic signals, and the asymptotic optimality of its performance is established through the asymptotic properties of block Hermitian Toeplitz matrices.
KW - Block Toeplitz matrices
KW - Error exponent
KW - Frequency-domain correlation
KW - Gaussian stochastic signal
KW - Quadratic detection
KW - Spectral mask
UR - http://www.scopus.com/inward/record.url?scp=77955674926&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77955674926&partnerID=8YFLogxK
U2 - 10.1109/TSP.2009.2035990
DO - 10.1109/TSP.2009.2035990
M3 - Article
AN - SCOPUS:77955674926
SN - 1053-587X
VL - 58
SP - 969
EP - 979
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
IS - 3 PART 1
ER -